BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Sphere
BornAgain
≻ git-develop
≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Hard particles ≻ Sphere
A full sphere.
Sphere(R)
Parameters:
As for any other Form factor.
Class Sphere inherits from the interface class Formfactor.
Form factor is computed as
$$ F(\mathbf{q})=4\pi R^3 \exp(iq_z R) \dfrac{\sin(qR) - qR \cos(qR)}{(qR)^3} , $$ with the notation $$ q := \sqrt{q_x^2 + q_y^2+ q_z^2}. $$
Volume has been validated against $$ V=\dfrac{4\pi}{3} R^3. $$
More general:
Truncated shapes:
Scattering by uncorrelated spheres for horizontal incidence:
Generated by Examples/sas/sas-ff.py
(particle_geometry=Sphere),
Examples/fq/Sphere.py
.
This form factor is well known; it goes back to Lord Rayleigh. In IsGISAXS, it has been implemented as form factor “Full sphere” Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.35; Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 226. In BornAgain, named “FullSphere” up to version 1.19.